A lot of babies break out in a sort of infant acne (but it can be other places besides the face). It's usually earlier than 4 months but if your son didn't go through it before, it could be related to that now. They look a lot like little pimples. Usually it just lasts a few weeks and we all joked that we just didn't take any baby pictures.
However, your child's rash seems to be more than that. Do the bumps appear irritated? Does he seem itchy or uncomfortable, cranky, feverish? It he trying to rub it with his hand, particularly on his face? If so, I'd give the doctor's weekend number a call - they may suggest something like infant benadryl for the itch and they will tell you the Have you switched to new clothing or bedding now that the weather is warmer? Sometimes a fabric can have a flame retardant on it or some detergent residue.
Have you tried a new food or formula? Put him on rice cereal? Maybe it's too soon for that in that his body isn't ready. My pedi put my son on some rice cereal at 4 months - I know it sounds early but some kids are "prescribed" that at an earlier age if they aren't gaining weight. And sometimes little bodies aren't ready for a new food and get a reaction? Some kids have to go from dairy to soy. And food sensitivities can cause the sort of reaction you are talking about.
Is he just hot? A heat rash can come at any time, not necessarily related to a helmet. Dress him as you would yourself, with just a little more since he's not running around yet and building up body heat. Don't overdress him but of course you don't want him to be cold.
How about detergent or fabric softener? Change to a dye-free, scent-free version or just wash in plain water and see what happens.
You don't have a dog or outdoor cat that got into any early poison ivy do you?
If it's a reaction to something he's eating, the topical baby oil or vaseline won't work. I'm surprised you were told to use either one. The sheets must be a mess! Vaseline is a petroleum product and some people can't tolerate it. Both products keep the skin from breathing so I'm not sure it's a great idea. It's not working anyway so I'd stop with all lotions or topical applications unless the pediatrician tells you to use something medicinal.
If it's a reaction to internal things (food/formula), then the problem starts inside and can't be fixed from the outside. Sometimes putting more stuff on it can cause more problems and make it spread. Don't use baby powder anywhere - it can cause a yeast infection. A lot of parents use that when they think their child is too hot or when there seems to be too much moisture (or to counteract a rash in the diaper area), and then it causes a new problem.
If he doesn't have a fever or seem really miserable, it's not an emergency. I wouldn't go to the ER or anything. If he seems uncomfortable, I'd definitely call the doctor - there's always a pediatrician on call for the weekend and phone consults are a lot more helpful than a weekend of worrying. If he's fine in every other way, I'd call on Monday morning.
You might try some plain cornstarch or oatmeal in his bath water - that can help an itch. And just bathe with plain water for now, no soap.
Good luck!